When Joseph Cadby (ref22) was married in 1838 his father's name is not given.
From the 1851 Census Joseph (22) was born in Birmingham aobut 1815.

There are two possible baptisms but it appears that one of these children died in infancy.
Therefore it has been assumed that Joseph is the son of James (ref44) and Mary (ref45) Cadby.
Without corroborating information and bearing in mind that the census could be inaccurate or that there could be unrecorded baptisms this identification is fairly weak.

The fact that James' name is not given in 1838 suggests he may have died by then.
The first child of James and Mary was apparently born in 1807, so they were presumably themselves born in the 1770s or 1780s.

When Joseph was married in 1838 his father's name was not given.  This could be because James had already died by that time.

There was a burial for a James Cadby at St Mary's Birmingham - 14th Jan 1829.
The deceased was 57 years old (born c1772) of James Street.
This is the most likely death from the records available.
It would mean that James was in his forties when Joseph was born and 35 when Mary was born.
In the 1821 and 1830 Trades Directories James Cadby of 3 James Street is listed as a Plater and manufacturer of plated wares.

There was a burial for James Cadby at St Philip Birmingham - 12 May 1819.
The deceased was 40 years old (born c1779) of the Workhouse.
This is a possible death - though less likely, given that his wife and other family were still around.

There was a burial for James Cadby at St Paul, Birmingham - 29 Dec 1858.
The deceased was 76 years old (born c1782) of Mount Street. This seems to be a different family.

There is a James Cadby, Caster, in the 1851 Census on Charlotte Street. He was born in Devizes, age given as 66.
His wife, Sarah, is listed as 10 years older and born in Staffordshire.
	This family is at the same address in the 1841 Census when his rounded age is given as 50.

There is a James Cadby at 40 Mount Street in the 1851 Census who was born in Birmingham in about 1816.  This would seem to be James Cadby the son of Ann and James Cadby baptised at St Philip Birmingham and therefore a different person.
He was aged 35 married to Mary Ann (who was born in West Bromwich) and a son, Joseph born about 1814 in West Bromwich, plus son John and daughter Sarah.

There is a Mary Cadby aged 70 in the 1841 Census - hence born about 1771. She could be the mother of Joseph.
She is living with Isaac Cadby, aged 20 in the home of Edward and Ann Rose.
Isaac seems to have been imprisoned later that year for 6 months and age given as 25.
There is a possible death for this Mary - 1845-Q4 Birmingham vol 16	page 166
 

There are several registers some of which are largely duplicates.

RG4/3325 begins:
The New Jerusalem Temple and the New Jerusalem Church being of the New Jerusalem church denomination situate in Summer Lane Birmingham in the County of Warwick founded about the year 1791.

RG4/3927
"In this register Cabda, Cabday and Cadby are the same individual, Cadby is the proper name."
"24 Swedenbourgians I"

Mary daughter of James and Mary Cabda		born 13 August 1807	Birmingham
							bapt. Sep 6th 1807   by William Faraday, Minister

Benjamin daughter of James and Mary Cabda		born 22 Apr 1810	Birmingham
							Bapt July 1 1810   by Joseph Proud, Minister

Isaac son of James and Mary Cadby			born 23 Dec 1812	Birmingham
(seems to say 'baptized privately')			bapt. 4 Jany 1813  by  Willaim Faraday 

Joseph son of Jas and Mary Cadby			born 16 May 1815	Birmingham
							Bapt. 11 Jun 1815 by Rev J Proud

On the previous page is says 'Rev J Proud of York Street Chapel, St. James' Square, London.'

RG9/3509 (which begins 1824) states:
Register of Baptisms according to the Form to be Directed to be used by the Seventeenth General Conference of the New Church signifies The New Jerusalem in Revelation held at Birmingham 1824.
  

Birmingham Journal 1 December 1827 - page 1, column 4
PARTNERSHIPS DISSOLVED
...Stephen Ward and James Cadby, Birmingham, casters and platers of metal